E yo J 
third, or CK = 839286755214, &c. That is, if the radius of the 
circle, by which a Gothic arch is defcribed, be to the interval of 
the capitals from which it fprings, as 1 to ,321426489572, the 
Gothic and femicircular arch of equal fpan will be alfo of equal 
ftrength. 
18. Hence therefore, a Gothic arch whofe radius of curvature is 
equal to the interval between the pillars, which is the ufual man- 
ner of defcription, is the weakeft of all Gothic arches of that 
fpan. According as the centre from which it is defcribed moves 
on either fide, in an horizontal line, the ftrength of the arch 
increafes: if it moves towards the middle point of the interval 
of the pillars, the ftrength increafes till the centre arrives at K, 
when the Gothic arch becomes. a femicircle. But if the centre 
moves in the contrary direction, the ftrength of the arch in- 
creafes without limit. 
19. Mons. Gautier therefore is too general in his affertion 
when he fays, that the Gothic arch is ftronger than the femi- 
circle; as this is true only in certain cafes, to wit, when the 
radius by which it is defcribed exceeds the fpan in the ratio of 
1 to 1321426489572, very nearly; in all other cafes it is weaker. 
We may obferve alfo, that Sir Henry Wotton is not fufficiently 
. warranted in his cenfure of this arch, when he fays, that “ thefe 
‘« kind of arches, both for the natural imbecility of the acute angles, 
“ as likewife for their uncomelinefs, ought to be exiled from all 
“« judicious eyes, and left to their firft inventors, the Goths and 
“« Lombards, amongft other reliques of the barbarous age.” As to 
its. 
